This article is cited in 1 paper

New Faddeev–Niemi-type variables for the static Yang–Mills theory

M. P. Kisielowski<sup>ab

a</sup> Institute of Theoretical Physics, University of Warsaw, Warsaw, Polland
^b St.~Petersburg Department of Steklov Institute of Mathematics, RAS, St. Petersburg, Russia

Abstract: Faddeev and Niemi introduced a nonlinear sigma model as a natural extension of the Faddeev $SU(2)$ chiral model. The field variables in the extended model are two chiral fields taking values in $SU(3)/(U(1)\times U(1))$ and $SU(3)/(SU(2)\times U(1))$. Shabanov showed that the energy functional of the extended model is bounded from below by a topological invariant and can therefore support knotlike excitations and a mass gap. We introduce new variables of the Faddeev–Niemi type for the static $SU(3)$ Yang–Mills theory, which reveal a structure of a nonlinear sigma model in the Lagrangian.

Keywords: Yang–Mills field, Faddeev–Niemi variables, stringlike soliton, maximal Abelian gauge fixing, Skyrme–Faddeev model.

Received: 09.12.2012

DOI: 10.4213/tmf8458

 English version: Theoretical and Mathematical Physics, 2013, 176:2, 1016–1043

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